Given:
sin theta = -4/5
cos theta >0
Since sin is negative and cos is positive, theta lies in the 4th quadrant. All trigonometric ratios, except cos and sec are negative in the fourth quadrant.
Therefore, tan is also negative.
sin theta = Perpendicular/Hypotenuse
Therefore, perpendicular = 4 units and hypotenuse =5 units.
According to Pythagorean theorem, in a right triangle, the sum of squares of the legs of a right triangle is equal to the square of the hypotenuse.
So, in a right triangle ABC, if AB is the perpendicular, BC is the adjacent side and AC is the hypotenuse, then
AC^2 = AB^2 + BC^2
BC^2=AC^2-AB^2
BC^2= 5^2 - 4^2
=25 - 16
BC ^2 = 9
BC = 3 units
Adjacent side = 3 units
We know that tan theta = perpendicular/Adjacent
=4/3
since tan is negative in the 4th quadrant,
tan theta =-4/3
